2. Answer the questions to the text.

1. What are the main characteristics of thinking?

2. What is thinking in its most general sense?

3. Which process does the term “judgment” refer to?

4. What do the goals determine?

5. What does a subgoal mean?

6. What can evidence consist of?

7. What is the end result of the search process?

8. What is the relationship among the elements of thinking?

2. Choose the facts to prove that:

1. We search for certain objects and then we make inferences from and about them.

2. We search for three kinds of objects — possibilities, evidence and goals.

Text 16 creative problem solving

People who are most successful at solving problems often are those who have many different sets at their disposal, and are able to represent the problem correctly and hence judge when to change sets or even to give up sets entirely. Simply put, they deal with problems creatively.

Many problems, of course, do not lend themselves to straightforward strategies but rely more on the use of flexible and creative thinking. The most famous example of creative problem solving comes from ancient Greece. The king asked the mathematician Archimedes (287— 212 B.C.) whether his crown was made of pure gold or had been adulterated with silver. Archimedes knew that an ounce of gold weighs more than an ounce of silver, but he did not know how to calculate the volume of a complicated object such as a crown. He worked on the problem day after day, but got nowhere. Then, one afternoon, he noticed that when he got into his bath, the water flowed over the edge of the tub. Suddenly he realized that he could calculate the volume of the crown by placing it in a basin of water and measuring how much water is displaced. Overjoyed by his sudden insight, he jumped out of his bath and ran naked through the streets of Syracuse shouting “Eurekd. I have found it.”

Centuries later, artists in France became dissatisfied with the representational painting of the day and puzzled over a better way to capture visual experience. One day they noticed that as the sun moves across the sky, the light on a haystack changes. Here was the solution! Instead of painting the haystack, they could paint the light. And so the Impressionist school of painting was born. The idea that light itself could be the subject of a painting had never occurred to their elders.

Creative solutions are not limited to science and art. What is smaller, more portable, and far less expensive than a bicycle; easier to navigate than a skateboard; does not require the strength and coordination of in-line skates; can be mounted or dismounted in a flash; provides recreation or transportation; and boasts a high-tech, urban image? The answer is a scooter, the fad that swept the country in 2000.

Convergent and Divergent Thinking

How many unusual uses can you think of for a brick? It’s easy to think of a few good uses but quite another task to come up with 50 or 60 distinct ones. Psychologists sometimes refer to this type of thinking as divergent thinking, in contrast to convergent thinking. A problem requiring convergent thinking has only one solution or a very few — for a example, a math problem. In such a case, the best approach is to examine the available facts, decide which are relevant, and look for a single, logical solution. By contrast, problems that have no single correct solution and that require a flexible, inventive approach call for divergent thinking — looking at the facts and expanding on them, imaging where different pieces of information might lead, and producing a number of possible solutions. Imagine, for example, that three hikers are lost in the woods. One argues that the only solution is to find their way back to the trail and uses a stick to begin sketching a rough map in the dirt. The second argues that the only solution is to find their way to the lake, which lies to the west, and begins fiddling with his compass. The third hiker — a divergent thinker — quietly gazes around, “letting his mind go.” Looking at the position of the sun, he decides they would not be able to make it to the lake before nightfall. He considers camping by the nearest stream, wonders if rangers conduct patrols, thinks about how they might send up a signal, and then finds himself staring at a tree. Suddenly he realizes that if he climbs the tree, he might find out where they are.

The Creative Process

Because creative problem solving requires thinking up new and original ideas, the process is not always aided by planning and the deliberate use of problem-solving strategies. Solutions to many problems rely on insight, a seemingly arbitrary flash “out of the blue” that solves a problem. Many of us have had the experience of suddenly seeing the way to a solution that previously had seemed all but impossible. Henri Poincare, the French mathematician, described his discovery of a new set of geometric principles this way:

Twas very ignorant; every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations and reached no results.... One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds. I felt them collide until pairs interlocked, so to speak, making a stable combination. By the next morning I had established the existence of a new class ofFuschian functions.

Poincare, 1924

Many people have provided strikingly similar accounts of their own processes of creative thinking. Drawing on heuristics, algorithms, and the expertise, they simply cannot come up with the solution to their problem. Then, as if by magic, the solution suddenly “pops into their heads, ” often after they’ve stopped working on the problem for a while. Therefore, if you simply cannot arrive at a solution to a problem after careful preparation and step-by-step efforts at problem solving, try to stop thinking about the problem for a while and return to it later, approaching it from a new angle. Sometimes you get so enmeshed in the details of a problem that you lose sight of the obvious. Taking a rest from a problem may allow you to discover a fresh approach.

Another creative strategy is to redefine the problem. It is easy to look at problems just as they are presented to us — to assume, for example, that we cannot work in more than two dimensions when solving the kitchen match problem. For example, if your business is losing money, you might sit down to figure out how to cut costs. But by defining the solution narrowly as cost cutting, you have ruled out the possibility that the best way to stop losing money might be to figure out creative ways to increase income rather than to cut costs. Thus, a better representation of this problem would be to discover ways to cut costs or increase income or both.

These examples demonstrate the importance of developing a questioning attitude toward problems. Ask yourself, “What is the real problem here?” “Can the problem be interpreted in other ways?” By redefining the problem, you may find that you have opened up new avenues to creative solutions. And try to maintain an uncritical attitude toward potential solutions: Don’t reject a potential solution because at first it seems not to be ideal for that problem. On closer examination,

the solution may turn out to be effective, or it may suggest similar solutions that would work. That is the rationale behind the technique called brainstorming. When solving a problem, generate lots of ideas without evaluating them prematurely. Only after lots of ideas have been collected should you review and evaluate them.